Chapter 9.5, Problem 31AE

Solar Energy The amount of energy collected by a solar panel depends on the intensity of the sun’s rays and the area of the panel. Let the vector I represent the intensity, in watts per square centimeter, having the direction of the sun’s rays. Let the vector A represent the area, in square centimeters, whose direction is the orientation of a solar panel. See the figure. The total number of watts collected by the panel is given by $\text{W}=\left|\text{I}\cdot \text{A}\right|$.

Suppose that $\text{I}=\langle -0.02,-0.01\rangle \text{and}\text{A}\text{=}\langle 300,400\rangle$.

(a) Find $\Vert \text{I}\Vert \text{and}\Vert \text{A}\Vert$, and interpret the meaning of each.

(b) Compute W and interpret its meaning.

(c) If the solar panel is to collect the maximum number of watts, what must be true about I and A?